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Diketahui vektor dan . Tentukan a. Proyeksi skal...

Diketahui vektor u with rightwards arrow on top equals 5 i plus 2 j minus 8 k dan v with rightwards arrow on top equals 3 i minus 2 j plus 6 k. Tentukan

a. Proyeksi skalar ortogonal 2 u with rightwards arrow on top pada v with rightwards arrow on top

Jawaban:

Pertama kita tentukan vektor 2 u with rightwards arrow on top :

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 u with rightwards arrow on top end cell equals cell 2 open square brackets table row 5 row 2 row cell negative 8 end cell end table close square brackets end cell row blank equals cell open square brackets table row 10 row 4 row cell negative 16 end cell end table close square brackets end cell end table

Iingat rumus Proyeksi skalar ortogonal u pada v

equals open vertical bar fraction numerator u with rightwards arrow on top times v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar end fraction close vertical bar 

Sehingga,  royeksi skalar ortogonal 2 u with rightwards arrow on top pada v with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell open vertical bar fraction numerator stack 2 u with rightwards arrow on top times v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator open square brackets table row 10 row 4 row cell negative 16 end cell end table close square brackets times open square brackets table row 3 row cell negative 2 end cell row 6 end table close square brackets over denominator square root of 3 squared plus open parentheses negative 2 close parentheses squared plus open parentheses 6 close parentheses squared end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator 30 minus 8 minus 96 ‬ over denominator square root of 9 plus 4 plus 36 end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 74 over denominator square root of 49 ‬ end root end fraction close vertical bar end cell row blank equals cell 74 over 7 end cell end table 

Jadi, Proyeksi skalar ortogonal 2 u with rightwards arrow on top pada v with rightwards arrow on topadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 74 over 7 end cell end table

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